Every circle has a constant width; that is, the distance between any pair of parallel lines touching the circle on opposite sides is always the same. A triangle, a rectangle, or an oval, on the other hand, do not have a constant width. This means, for example, that if you were to make a manhole cover using one of these shapes, you could turn the cover so that it would fall through, while a circular cover would not fall through. The Reuleaux triangle is the simplest noncircular curve that has a constant width. Any regular polygon with an odd number of sides can be used as the basis for a Reuleaux polygon of constant width.

Many internal combustion engines are described as "four-stroke" engines. This refers to the fact that the engine goes through 4 distinct stages. In the first stage, the intake stroke, air is taken into the engine and mixed with fuel. In the second stage, the compression stroke, the fuel-air mixture is compressed into a small space. Compression in the second stage leads to the production of power when the compressed fuel-air mixture is ignited, or combusted, and so expands to provide power in the 3rd stage, the combustion stroke. In the fourth stage, the exhaust stroke, the remains of the combustion of the fuel-air mixture are expelled from the engine.

A Wankel rotary engine is a type of 4-stroke engine. Refer to the cross-section of the Wankel engine that appears on page 639. The Reuleaux triangle in the diagram represents the rotor of a Wankel rotary engine. As the rotor turns in the engine housing, the three vertices of the triangle stay in constant contact with the walls of the housing.

Due to the shape of the engine housing, the size of each of the three chambers created by the rotor changes as the rotor rotates. The chamber is large when air is taken in and mixed with fuel, and decreases in size to compress the fuel-air mixture. The chamber is smallest when the mixture is combusted, which provides powers to turn the rotor. The combusted mixture expands into the increased space made by the rotor's continued turning, and is exhausted.

The Wankel engine, named for German engineer Felix Wankel, who first received a patent for the rotary combustion engine in 1929, has several advantages over the conventional internal combustion engine. It is simpler, requiring 40% fewer moving parts, and has about a third less bulk than a conventional engine. It also vibrates less, produces more power for a given engine weight, and can run at high speeds for long periods of time. The first successful prototype of a Wankel engine was built in the mid-1950s. During the late 1960s and the 1970s, automobiles with Wankel rotary engines became popular. But partially because of difficulties with fuel efficiency and emissions, production waned, and the last mass-produced cars with Wankel engines rolled off the assembly line in 1996.

Research and development of the Wankel engine, however, continue. A prototype sports car meeting Japan's low-emissions standards has been built. A two-passenger aircraft that can take off and land vertically, hover like a helicopter, and fly at nearly 300 miles per hour has even been developed around a rotary engine. Also, Wankel engines appear to be ideal for burning hydrogen as a fuel, a fact that may boost its popularity as development continues on automobiles powered by alternatives to fossil fuels.